Question

Estimate the wavelength corresponding to maximum emission from each of the following surfaces: The Sun, a Tungsten filament at 2500°C, molten Aluminum, human body at 37°C, and a cryogenically cooled Silicon chip at -200°C.

Answer 1

The estimated wavelengths corresponding to maximum emission from the given surfaces are: 520 nm for the Sun, 1082 nm for a Tungsten filament at 2500°C, 9677 nm for the human body at 37°C, and 41038 nm for a cryogenically cooled Silicon chip at -200°C.

Step-by-step explanation:

According to Wien's law, the wavelength of maximum emission from a surface is inversely proportional to its temperature. The formula is λ = 3 x 10^6 / T, where λ is the wavelength in nanometers (nm) and T is the temperature in Kelvin (K).

Using this formula, we can estimate the wavelengths corresponding to maximum emission from each surface:

• The Sun: Since the temperature of the Sun is approximately 5778 K, the estimated wavelength is λ = 3 x 10^6 / 5778 ≈ **520 nm**.
• Tungsten filament at 2500°C: Convert 2500°C to K by adding 273.15, giving 2773.15 K. The estimated wavelength is λ = 3 x 10^6 / 2773.15 ≈ **1082 nm**.
• Molten Aluminum: Since no temperature is given for molten aluminum, we cannot provide an estimate.
• Human body at 37°C: Convert 37°C to K, giving 310 K. The estimated wavelength is λ = 3 x 10^6 / 310 ≈ **9677 nm**.
• Cryogenically cooled Silicon chip at -200°C: Convert -200°C to K, giving 73.15 K. The estimated wavelength is λ = 3 x 10^6 / 73.15 ≈ **41038 nm**.